On Equilibrium (-1799)

"Equal weights at equal distances are in equilibrium and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance." (Archimedes, "On the Equilibrium of Planes" Vol. I, 3rd century BC)

"Two magnitudes whether commensurable or incommensurable, balance at distances reciprocally proportional to the magnitudes." (Archimedes, "On the Equilibrium of Planes" Vol. I, 3rd century BC)

"Inequality is the cause of all local movements. There is no rest without equality." (Leonardo da Vinci, Codex Atlanticus, 1478)

"There must be a double method for solving mechanical problems: one is the direct method founded on the laws of equilibrium or of motion; but the other one is by knowing which formula must provide a maximum or a minimum. The former way proceeds by efficient causes: both ways lead to the same solution, and it is such a harmony which convinces us of the truth of the solution, even if each method has to be separately founded on indubitable principles. But is often very difficult to discover the formula which must be a maximum or minimum, and by which the quantity of action is represented.” (Leonhard Euler, “Specimen de usu observationum in mathesi pura", Novi Commentarii academiae scientiarum Petropolitanae 6, 1756/57)

"Statics is the science of the equilibrium of forces. In general, force or power is the cause, whatever it may be, which induces or tends to impart motion to the body to which it is applied. The force or power must be measured by the quantity of motion produced or to be produced. In the state of equilibrium, the force has no apparent action. It produces only a tendency for motion in the body it is applied to. But it must be measured by the effect it would produce if it were not impeded. By taking any force or its effect as unity, the relation of every other force is only a ratio, a mathematical quantity, which can be represented by some numbers or lines. It is in this fashion that forces must be treated in mechanics." (Joseph-Louis de Lagrange, "Mechanique Analytique", 1788)

On Gravity I

"Until now, physical theories have been regarded as merely models with approximately describe the reality of nature. As the models improve, so the fit between theory and reality gets closer. Some physicists are now claiming that supergravity is the reality, that the model and the real world are in mathematically perfect accord." (Paul C W Davies, "Superforce", 1984)

"To build matter itself from geometry - that in a sense is what string theory does. It can be thought of that way, especially in a theory like the heterotic string which is inherently a theory of gravity in which the particles of matter as well as the other forces of nature emerge in the same way that gravity emerges from geometry. Einstein would have been pleased with this, at least with the goal, if not the realization. [...] He would have liked the fact that there is an underlying geometrical principle - which, unfortunately, we don’t really yet understand." (David Gross, [interview] 1988)

"No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. […] because any unified field theory first must absorb the Riemannian geometry of Einstein’s theory and the Lie groups coming from quantum field theory. […] The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity." (Michio Kaku, "Hyperspace", 1995)

"Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a 'force' has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed." (Michio Kaku, "Hyperspace", 1995)

"Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed, supersymmetry is one of the basic requirements of 'string theory', which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces. Discovery of supersymmetry would would certainly give string theory an enormous boost." (Edward Witten, [preface to (Gordon Kane, "Supersymmetry: Unveiling the Ultimate Laws of Nature", 2000) 1999)

"Combine general relativity and quantum theory into a single theory that can claim to be the complete theory of nature. This is called the problem of quantum gravity." (Lee Smolin, "The Trouble with Physics: The Rise of String Theory, The Fall of a Science and What Comes Next", 2006)

"[…] there’s atomic physics - electrons and protons and neutrons, all the stuff of which atoms are made. At these very, very, very small scales, the laws of physics are much the same, but there is also a force you ignore, which is the gravitational force. Gravity is present everywhere because it comes from the entire mass of the universe. It doesn’t cancel itself out, it doesn’t have positive or negative value, it all adds up." (Michael F Atiyah, [interview] 2013)

"String theory today looks almost fractal. The more closely people explore any one corner, the more structure they find. Some dig deep into particular crevices; others zoom out to try to make sense of grander patterns. The upshot is that string theory today includes much that no longer seems stringy. Those tiny loops of string whose harmonics were thought to breathe form into every particle and force known to nature (including elusive gravity) hardly even appear anymore on chalkboards at conferences." (K C Cole, "The Strange Second Life of String Theory", Quanta Magazine", 2016) [source]

"Even though it is, properly speaking, a postprediction, in the sense that the experiment was made before the theory, the fact that gravity is a consequence of string theory, to me, is one of the greatest theoretical insights ever." (Edward Witten)

"String theory is extremely attractive because gravity is forced upon us. All known consistent string theories include gravity, so while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory." (Edward Witten)

Hermann von Helmholtz - Collected Quotes

"There is a kind, I might almost say, of artistic satisfaction, when we are able to survey the enormous wealth of Nature as a regularly ordered whole - a kosmos, an image of the logical thought of our own mind." (Hermann von Helmholtz. "On the Conservation of Force", 1862)

"When I have before my eyes a pair of stereoscopic drawings which are hard to combine, it is difficult to bring the lines and points that correspond, to cover each other, and with every little motion of the eyes they glide apart. But if I chance to gain a lively mental image (Anschauungsbild) of the represented solid form (a thing that often occurs by lucky chance), I then move my two eyes with perfect certainty over the figure without the picture separating again." (Hermann von Helmholtz, "Tonempfindungen" ["Sensations of Tone"], 1863)

"Thus representations of the external world are images of the lawlike temporal succession of natural events, and if they are correctly formed in accordance with the laws of our thinking, and we are able correctly to translate them back again into actuality through our actions, then the representations that we have are also the uniquely true [ones] for our faculty of thought; all others would be false." (Hermann von Helmholtz, "Handbuch der physiologischen Optik" Vol. 3, 1867)

"Isolated facts and experiments have in themselves no value, however great their number may be. They only become valuable in a theoretical or practical point of view when they make us acquainted with the law of a series of uniformly recurring phenomena, or, it may be, only give a negative result showing an incompleteness in our knowledge of such a law, till then held to be perfect." (Hermann von Helmholtz, "The Aim and Progress of Physical Science", 1869)

"A law of nature, however, is not a mere logical conception that we have adopted as a kind of memoria technical to enable us to more readily remember facts. We of the present day have already sufficient insight to know that the laws of nature are not things which we can evolve by any speculative method. On the contrary, we have to discover them in the facts; we have to test them by repeated observation or experiment, in constantly new cases, under ever-varying circumstances; and in proportion only as they hold good under a constantly increasing change of conditions, in a constantly increasing number of cases with greater delicacy in the means of observation, does our confidence in their trustworthiness rise." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"It [geometry] escapes the tedious and troublesome task of collecting experimental facts, which is the province of the natural sciences in the strict sense of the word; the sole form of its scientific method is deduction." (Hermann von Helmholtz, "Popular Lectures on Scientific Subjects", 1873)

"A metaphysical conclusion is either a false conclusion or a concealed experimental conclusion." (Hermann von Helmholtz, "On Thought in Medicine", 1877)

"Mathematics and music, the most sharply contrasted fields of scientific activity which can be found, and yet related, supporting each other, as if to show forth the secret connection which ties together all the activities of our mind, and which leads us to surmise that the manifestations of the artist's genius are but the unconscious expressions of a mysteriously acting rationality." (Hermann von Helmholtz, "Vorträge und Reden", Bd. 1, 1884)

"I have been able to solve a few problems of mathematical physics on which the greatest mathematicians since Euler have struggled in vain. [...] But the pride I might have held in my conclusions was perceptibly lessened by the fact that I knew that the solution of these problems had almost always come to me as the gradual generalization of favorable examples, by a series of fortunate conjectures, after many errors. I am fain to compare myself with a wanderer on the mountains who, not knowing the path, climbs slowly and painfully upwards and often has to retrace his steps because he can go no further—then, whether by taking thought or from luck, discovers a new track that leads him on a little till at length when he reaches the summit he finds to his shame that there is a royal road by which he might have ascended, had he only the wits to find the right approach to it. In my works, I naturally said nothing about my mistake to the reader, but only described the made track by which he may now reach the same heights without difficulty." (Hermann von Helmholtz, 1891)

"[In mathematics] we behold the conscious logical activity of the human mind in its purest and most perfect form. Here we learn to realize the laborious nature of the process, the great care with which it must proceed, the accuracy which is necessary to determine the exact extent of the general propositions arrived at, the difficulty of forming and comprehending abstract concepts; but here we learn also to place confidence in the certainty, scope and fruitfulness of such intellectual activity." (Hermann Helmholtz, "Vorträge und Reden", 1896)

"In proportion as the range of science extends, its system and organization must be improved, and it must inevitably come about that individual students will find themselves compelled to go through a stricter course of training than grammar is in a position to supply." (Hermann von Helmholtz, "On the Relation of Natural Science to Science in general", Popular Lectures on Scientific Subjects, 1900)

Frank Wilczek - Collected Quotes

"As the idea of permanence of objects has faded, the idea of permanence of physical laws has become better established and more powerful." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987) 

"The main problem with many nonscientific world models is the vigor with which they insist upon their rightness. Once a world model claims to be completely right, it is no longer open to any changes. […] Closed systems can be comforting, but they are limited. […] It's not the best we can do. Neither is extreme 'open-mindednesss' that slides into 'empty headedness' - the ideal that we can never really know anything."  (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987) 

"The most abstract conservation laws of physics come into their being in describing equilibrium in the most extreme conditions. They are the most rigorous conservation laws, the last to break down. The more extreme the conditions, the fewer the conserved structures. [...] In a deep sense, we understand the interior of the sun better that the interior of the earth, and the early stages of the big bang best of all."  (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987) 

"The whole idea of science is really to listen to nature, in her own language, as part of a continuing dialogue." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987) 

"What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation." (Frank Wilczek, "Longing for the Harmonies: Themes and Variations from Modern Physics", 1987)

"In physics, your solution should convince a reasonable person. In math, you have to convince a person who's trying to make trouble. Ultimately, in physics, you're hoping to convince Nature. And I've found Nature to be pretty reasonable." (Frank Wilczek, Fantastic Realities: 49 Mind Journeys and a Trip to Stockholm, 2006) 

"An ordinary mistake is one that leads to a dead end, while a profound mistake is one that leads to progress. Anyone can make an ordinary mistake, but it takes a genius to make a profound mistake." (Frank Wilczek,"The Lightness of Being – Mass, Ether and the Unification of Forces", 2008) 

"Knowing how to calculate something is not the same as understanding it. Having a computer to calculate the origin of mass for us may be convincing, but is not satisfying. Fortunately we can understand it too." (Frank Wilczek,"The Lightness of Being – Mass, Ether and the Unification of Forces", 2008) 

"We evolved to be good at learning and using rules of thumb, not at searching for ultimate causes and making fine distinctions. Still less did we evolve to spin out long chains of calculation that connect fundamental laws to observable consequences. Computers are much better at it!" (Frank Wilczek,"The Lightness of Being – Mass, Ether and the Unification of Forces", 2008) 

"The happy coincidences between life’s requirements and nature’s choices of parameter-values might be just a series of flukes, but one could be forgiven for beginning to suspect that something deeper is at work. That suspicion is the first deep root of anthropic reasoning." (Frank Wilczek, "Multiversality", 2013) 

"Ironically, conventional quantum mechanics itself involves a vast expansion of physical reality, which may be enough to avoid Einstein Insanity. The equations of quantum dynamics allow physicists to predict the future values of the wave function, given its present value. According to the Schrödinger equation, the wave function evolves in a completely predictable way. But in practice we never have access to the full wave function, either at present or in the future, so this 'predictability' is unattainable. If the wave function provides the ultimate description of reality - a controversial issue!" (Frank Wilczek, "Einstein’s Parable of Quantum Insanity", 2015) 

On Equilibrium (1875-1889)

"Any system in stable chemical equilibrium, subjected to the influence of an external cause tends to change either its temperature or its condensation (pressure, concentration, number of molecules in unit volume), either as a whole or in some of its parts, can only undergo such internal modifications as would, if produced alone, bring about a change of temperature or of condensation of opposite sign to that resulting from the external cause." (Henri L Le Chatelier, "A General Statement of the Laws of Chemical Equilibrium", Comptes rendus Vol. 99, 1884)

"Every situation is an equilibrium of forces; every life is a struggle between opposing forces working within the limits of a certain equilibrium." (Henri-Frédéric Amiel, "Amiel's Journal", 1885)

"Plasticity, then, in the wide sense of the word, means the possession of a structure weak enough to yield to an influence, but strong enough not to yield all at once. Each relatively stable phase of equilibrium in such a structure is marked by what we may call a new set of habits." (William James, "The Laws of Habit", 1887) 

"Every change of one of the factors of an equilibrium occasions a rearrangement of the system in such a direction that the factor in question experiences a change in a sense opposite to the original change." (Henri L Le Chatelier, "Recherches Experimentales et Theoriques sur les Equilibres Chimiques" ["Experimental and Theoretical Research on Chemical Equilibria"], Annales des Mines 8, 1888)

"In every symmetrical system every deformation that tends to destroy the symmetry is complemented by an equal and opposite deformation that tends to restore it. […] One condition, therefore, though not an absolutely sufficient one, that a maximum or minimum of work corresponds to the form of equilibrium, is thus applied by symmetry." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)

"That branch of physics which is at once the oldest and the simplest and which is therefore treated as introductory to other departments of this science, is concerned with the motions and equilibrium of masses. It bears the name of mechanics." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)

"The whole aspect of the universe changes with this new conception. The idea of force governing the world, of pre-established law, preconceived harmony, disappears to make room for the harmony that [Charles] Fourier had caught a glimpse of: the one which results from the disorderly and incoherent movements of numberless hosts of matter, each of which goes its own way and all of which hold each other in equilibrium." (Peter Kropotkin, "Anarchism: Its Philosophy and Ideal", 1896)

On Equilibrium (1950-1959)

"Now a system is said to be at equilibrium when it has no further tendency to change its properties." (Walter J Moore, "Physical chemistry", 1950)

"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"Equilibrium requires that the whole of the structure, the form of its elements, and the means of interconnection be so combined that at the supports there will automatically be produced passive forces or reactions that are able to balance the forces acting upon the structures, including the force of its own weight."  (Eduardo Torroja, "Philosophy of Structure", 1951) 

"[…] there are three different but interconnected conceptions to be considered in every structure, and in every structural element involved: equilibrium, resistance, and stability." (Eduardo Torroja, "Philosophy of Structure" , 1951) 

"Business-cycle theorists concerned themselves with why the economy naturally generated fluctuations in employment and output, [while the rest of the profession] continued to operate on the assumption that full employment was the natural, equilibrium position for the economy." (Robert A Gordon, "Business Fluctuations", 1952)

"Biological communities are systems of interacting components and thus display characteristic properties of systems, such as mutual interdependence, self-regulation, adaptation to disturbances, approach to states of equilibrium, etc." (Ludwig von Bertalanffy, "Problems of Life", 1952)

"Every stable system has the property that if displaced from a state of equilibrium and released, the subsequent movement is so matched to the initial displacement that the system is brought back to the state of equilibrium. A variety of disturbances will therefore evoke a variety of matched reactions." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)

"The primary fact is that all isolated state-determined dynamic systems are selective: from whatever state they have initially, they go towards states of equilibrium. These states of equilibrium are always characterised, in their relation to the change-inducing laws of the system, by being exceptionally resistant." (W Ross Ashby, "Design for a Brain: The Origin of Adaptive Behavior", 1952)

"Multiple equilibria are not necessarily useless, but from the standpoint of any exact science the existence of a uniquely determined equilibrium is, of course, of the utmost importance, even if proof has to be purchased at the price of very restrictive assumptions; without any possibility of proving the existence of (a) uniquely determined equilibrium - or at all events, of a small number of possible equilibria - at however high a level of abstraction, a field of phenomena is really a chaos that is not under analytical control." (Joseph A Schumpeter, "History of Economic Analysis", 1954)

"Perhaps as important is the relation between the existence of solutions to a competitive equilibrium and the problems of normative or welfare economics." (Kenneth J Arrow & Gerard Debreu. "Existence of an equilibrium for a competitive economy", Econometrica: Journal of the Econometric Society, 1954)

"As shorthand, when the phenomena are suitably simple, words such as equilibrium and stability are of great value and convenience. Nevertheless, it should be always borne in mind that they are mere shorthand, and that the phenomena will not always have the simplicity that these words presuppose." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"Reversible processes are not, in fact, processes at all, they are sequences of states of equilibrium. The processes which we encounter in real life are always irreversible processes." (Arnold Sommerfeld, "Thermodynamics and Statistical Mechanics", Lectures on Theoretical - Physics Vol. V, 1956)

"Thus, if the whole is at a state of equilibrium, each part must be in a state of equilibrium in the conditions provided by the other. [...] the whole is at a state of equilibrium if and only if each part is at a state of equilibrium in the conditions provided by the other part. [...] No state (of the whole) can be a state of equilibrium unless it is acceptable to every one of the component parts, each acting in the conditions given by the others." (W Ross Ashby, "An Introduction to Cybernetics", 1956)

"It is clear to all that the animal organism is a highly complex system consisting of an almost infinite series of parts connected both with one another and, as a total complex, with the surrounding world, with which it is in a state of equilibrium. (Ivan P Pavlov, "Experimental psychology, and other essays", 1957)

"[Equilibrium] is a notion which can be employed usefully in varying degrees of looseness. It is an absolutely indispensable part of the toolbag of the economist and one which he can often contribute usefully to other sciences which are occasionally apt to get lost in the trackless exfoliations of purely dynamic systems." (Kenneth Boulding, The Skills of the Economist", Journal of Political Economy 67 (1), 1959)

"One of the most important skills of the economist, therefore, is that of simplification of the model." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)

"The ability to work with systems of general equilibrium is perhaps one of the most important skills of the economist - a skill which he shares with many other scientists, but in which he has perhaps a certain comparative advantage." (Kenneth Boulding, "The Skills of the Economist", Journal of Political Economy 67 (1), 1959)

On Metaphors VI

"Progress in truth - truth of science and truth of religion - is mainly a progress in the framing of concepts, in discarding artificial abstractions or partial metaphors, and in evolving notions which strike more deeply into the root of reality." (Alfred N Whitehead, "Religion in the Making", 1926)

"Science advances metaphorically. It does not proceed in an orthogenic fashion moving inexorably forward in a straight line. It does not radiate along many branches like a growing tree. It moves from one view to another by a large leap, preceded by a radical shift in the scientist’s mode of thought." (François Jacob, "The Logic of Life: A History of Heredity", 1970)

"Clever metaphors die hard. Their tenacity of life approaches that of the hardiest micro-organisms. Living relics litter our language, their raisons d’etre forever past, ignored if not forgotten, and their present fascination seldom impaired by the confusions they may create." (James R Moore, "The Post-Darwinian Controversies", 1979)

"Metaphor, the life of language, can be the death of meaning. It should be used in moderation, like vodka. Writers drunk on metaphor can forget they are conveying information and ideas." (Robert Fulford, 1996)

"So much of science consists of things we can never see: light ‘waves’ and charged ‘particles’; magnetic ‘fields’ and gravitational ‘forces’; quantum ‘jumps’ and electron ‘orbits’. In fact, none of these phenomena is literally what we say it is. Light waves do not undulate through empty space in the same way that water waves ripple over a still pond; a field is only a mathematical description of the strength and direction of a force; an atom does not literally jump from one quantum state to another, and electrons do not really travel around the atomic nucleus in orbits. The words we use are merely metaphors." (K C Cole, "On Imagining the Unseeable", Discover Magazine, 1982)

"Metaphor and simile are the characteristic tropes of scientific thought, not formal validity of argument." (Rom Harré, "Varieties of Realism", 1986)

"[…] mathematics does not come to us written indelibly on Nature’s Tablets, but rather is the product of a controlled search governed by metaphorical considerations, the premier instance being the heuristics of the conservation principles." (Philip Mirowski, "More Heat than Light: Economics as Social Physics: Physics as Nature’s Economics", 1989)

"Today’s quarks and leptons can be viewed as metaphors of the underlying reality of nature, though metaphors that are objectively and rationally defied and are components of theories that have great predictive power. And that’s the difference between the metaphors of science and those of myth: scientific metaphors work." (Victor J Stenger, "Physics and Psychics: The Search for a World Beyond the Senses", 1990)

"[…] we see from these formulations how difficult it is when we try to push new ideas into an old system of concepts belonging to an earlier philosophy, or, to use an old metaphor, when we attempt to put new wine into old bottles. Such attempts are always distressing, for they mislead us into continually occupying with the inevitable cracks in the old bottles, instead of rejoicing over the new wine." (Werner K Heisenberg)

Michael Faraday - Collected Quotes

"[…] it is always safe and philosophic to distinguish, as much as is in our power, fact from theory [...]" (Michael Faraday, "A Speculation Touching Electric Conduction and the Nature of Matter", Philosophical Magazine Vol. XXIV, 1844)

"How wonderful it is to me the simplicity of nature when we rightly interpret her laws and how different the convictions which they produce on the mind in comparison with the uncertain conclusions which hypothesis or even theory present." (Michael Faraday, [letter to Svanberg] 1850)

 "Hypotheses, treated as mere poetic fancies in one age, scouted as scientific absurdities in the next - preparatory only to their being altogether forgotten - have often, when least expected, received confirmation from indirect channels, and, at length, become finally adopted as tenets, deducible from the sober exercise of induction." (Michael Faraday, "The Subject Matter of a Course of Six Lectures on the Non-Metallic Elements", 1853)

"[…] in the pursuit of physical science, the imagination should be taught to present the subject investigated in all possible and even impossible views […]" (Michael Faraday, "Experimental Researches in Chemistry and Physics", 1859)

 "The world little knows how many of the thoughts and theories which have passed through the mind of a scientific investigator have been crushed in silence and secrecy; that in the most successful instances not a tenth of the suggestions, the hopes, the wishes, the preliminary conclusions have been realized." (Michael Faraday, "The Forces of Matter", 1860)

"As an experimentalist, I feel bound to let experiment guide me into any train of thought which it may justify; being satisfied that experiment, like analysis, must lead to strict truth if rightly interpreted; and believing also that it is in its nature far more suggestive of new trains of thought and new conditions of natural power." (Michael Faraday)

"I will simply express my strong belief, that that point of self-education which consists in teaching the mind to resist its desires and inclinations, until they are proved to be right, is the most important of all, not only in things of natural philosophy, but in every department of daily life." (Michael Faraday)

"Let the imagination go, guiding it by judgment and principle but holding it in and directing it by experiment." (Michael Faraday)

"Nothing is too wonderful to be true, if it be consistent with the laws of nature, and in such things as these, experiment is the best test of such consistency." (Michael Faraday)

"[Science] teaches us to be neglectful of nothing, not to despise the 

small beginnings [...] for the small often contains the great in princi￾ple, as the great does the small." (Michael Faraday)

"The more we can enlarge the number of anomalous facts and consequences the better it will be for the subject; for they can only remain anomalies to us while we continue in error." (Michael Faraday)

"The truth of science has ever had not merely the task of evolving herself from the dull and uniform mist of ignorance, but also that of the repressing and dissolving the phantoms of the imagination." (Michael Faraday)

On Chaos II

“We ought then to consider the present state of the universe as the effect of its previous state and as the cause of that which is to follow. An intelligence that, at a given instant, could comprehend all the forces by which nature is animated and the respective situation of the beings that make it up, if moreover it were vast enough to submit these data to analysis, would encompass in the same formula the movements of the greatest bodies of the universe and those of the lightest atoms. For such an intelligence nothing would be uncertain, and the future, like the past, would be open to its eyes.” (Pierre-Simon de Laplace, “Essai philosophique sur les probabilités”, 1814)

“Certainly, if a system moves under the action of given forces and its initial conditions have given values in the mathematical sense, its future motion and behavior are exactly known. But, in astronomical problems, the situation is quite different: the constants defining the motion are only physically known, that is with some errors; their sizes get reduced along the progresses of our observing devices, but these errors can never completely vanish.” (Jacques Hadamard, “Les surfaces à courbures opposées et leurs lignes géodésiques”, Journal de mathématiques pures et appliqués 5e (4), 1898) 

“In every important advance the physicist finds that the fundamental laws are simplified more and more as experimental research advances. He is astonished to notice how sublime order emerges from what appeared to be chaos. And this cannot be traced back to the workings of his own mind but is due to a quality that is inherent in the world of perception.” (Albert Einstein, 1932) 

“There is a maxim which is often quoted, that ‘The same causes will always produce the same effects.’ To make this maxim intelligible we must define what we mean by the same causes and the same effects, since it is manifest that no event ever happens more that once, so that the causes and effects cannot be the same in all respects. [...] There is another maxim which must not be confounded with that quoted at the beginning of this article, which asserts ‘That like causes produce like effects’. This is only true when small variations in the initial circumstances produce only small variations in the final state of the system. In a great many physical phenomena this condition is satisfied; but there are other cases in which a small initial variation may produce a great change in the final state of the system, as when the displacement of the ‘points’ causes a railway train to run into another instead of keeping its proper course.” (James C Maxwell, “Matter and Motion”, 1876)

"If a single flap of a butterfly's wing can be instrumental in generating a tornado, so all the previous and subsequent flaps of its wings, as can the flaps of the wings of the millions of other butterflies, not to mention the activities of innumerable more powerful creatures, including our own species." (Edward N Lorenz, [talk] 1972)

"If the flap of a butterfly’s wings can be instrumental in generating a tornado, it can equally well be instrumental in preventing a tornado." (Edward N Lorenz, [talk] 1972)

"The term ‘chaos’ currently has a variety of accepted meanings, but here we shall use it to mean deterministically, or nearly deterministically, governed behavior that nevertheless looks rather random. Upon closer inspection, chaotic behavior will generally appear more systematic, but not so much so that it will repeat itself at regular intervals, as do, for example, the oceanic tides." (Edward N Lorenz, "Chaos, spontaneous climatic variations and detection of the greenhouse effect", 1991)

"Unfortunately, recognizing a system as chaotic will not tell us all that we might like to know. It will not provide us with a means of predicting the future course of the system. It will tell us that there is a limit to how far ahead we can predict, but it may not tell us what this limit is. Perhaps the best advice that chaos ‘theory’ can give us is not to jump at conclusions; unexpected occurrences may constitute perfectly normal behavior." (Edward N Lorenz, "Chaos, spontaneous climatic variations and detection of the greenhouse effect", 1991) 

“[…] some systems […] are very sensitive to their starting conditions, so that a tiny difference in the initial ‘push’ you give them causes a big difference in where they end up, and there is feedback, so that what a system does affects its own behavior.” (John Gribbin, “Deep Simplicity”, 2004)